Section V.2: Magnitudes, Directions, and Components of a Vector
Exercises
Describe the direction of the following vectors, using angles in standard position. Round
any angles to one decimal place.
1. The vector that runs from the point (1,1) to (5,–2).
2. The vector that runs from the point (5,-2) to (1,1).
3. Compare your answers for #1 and #2. Why are they the same/different?
State the magnitude of the following vectors. Give exact answers.
4. The vector that runs from the point (1,1) to (5,–2).
5. The vector that runs from the point (5,–2) to (1,1).
6. Compare your answers for #4 and #5. Why are they the same/different?
Consider the four vectors in the diagram below.
y
A
B
x
C
D
7. Give the magnitude and direction (in standard position) for these vectors. Give exact
answers for the magnitudes and round any angles to the nearest degree.
8. Write the component form of each vector in the above diagram.
State the magnitude and direction of the following vectors. Give exact answers.
9. Bx = 35, By = 0
10. Fx = –16, Fy = –16
11. A = 3i – 3 3 j
12. A = –7j
State the magnitude and direction of the following vectors. Round your answers to the
nearest decimal place.
13. Ax = 2.3 m, Ay = 5.4 m
14. Ex = –16, Ey = 17
15. A = 1.1i – 2.7j
16. A = –6.5 i
Give the component form of the following vectors. Give exact answers in ijk notation.
17. A = 5, θ = 45º
18. A = 3, θ = 90º
19. A = 2, θ = 120º
20. A = 7, θ = 0
Give the component form of the following vectors in the form Ax and Ay. Round answers
to one decimal place.
21. A = 5, θ = 22º
22. A = 3, θ = –100º
Find a unit vector u in the same direction as the given vector. Give exact answers.
23. A = 4i – 3j
24. A = 7i
25. A = –2i + 2j
26. A = –7i – 24j
27. A = i –
3j
28. A = 5, θ = 22º (hint: don’t think too hard on this one)
Given that A = 3i – 4j and B is a vector with magnitude of 3 and direction 135º in
standard position, calculate the following. Leave your answers in whatever form you
prefer (it’s easiest to leave them in the form of the original vector).
29. 5A
30. –A
31. –B
32. 3B
33. What’s the terminal point of the vector B = – 2 i – 3 j which starts at the point (2,4)?
34. What’s the initial point of the vector B = 5 i – 8 j which ends at the point (3,–1)?
35. Write in ijk notation the vector that runs from the point (1,1) to (5,–2).
Sketch the following vectors on the accompanying grid.
36. A = 3j, starting at the point (1,–6)
37. B = –2i + j, starting at the point (5,–3)
38. C = –3j, starting at the point (5,–3)
39. D = –4i, starting at the point (5,–6)
40. E = 2i + j, starting at the point (1,–3)